GREEN'S FUNCTIONS IN PHYSICAL GEODESY AND THE COMPUTATION OF THE EXTERNAL GRAVITY FIELD AND THE GEODETIC BOUNDARY VALUE PROBLEM.
OHIO STATE UNIV RESEARCH FOUNDATION COLUMBUS INST OF GEODESY PHOTOGRAMMETRY AND CARTOGRAPHY
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Of the two main approaches to boundary value problems-the use of Greens functions and of integral equations--the latter approach has been chosen almost exclusively for the geodetic boundary value problem. The present report shows how Greens functions may be used for re-deriving known formulas and also for obtaining new results. Formulas for the third boundary value problem for the sphere are developed and then specialized to Stokes problem. As a limiting case, the boundary value problem for the plane is briefly considered. Then a formula for the variation of Greens function with the boundary surface is developed and applied to the problem of Molodensky. The main purpose of the present paper is to give formulas and, as an appendix, some estimates for the effect of topographic height on these computations. In addition, the paper presents connections between the determination of the external gravity field from surface data, which is related to the conventional boundary value problems of potential theory, and the determination of the earths physical surface itself, which is specifically geodetic boundary value problem.